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Stochastic barriers for the Wiener process and a mathematical model

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Part of the Lecture Notes in Mathematics book series (LNM,volume 939)

Abstract

Let {W(t), 0≤t<∞} be the standard Wiener process. The probabilities of the type P[sup0≤t≤TW(t)−f(t)≧0] have been extensively studied when f(t) is a deterministic function. This paper discusses the probabilities of the type P<Superscript>p0≤t≤TW(t)−[f(t)+X(t)]≧0</Superscript> when X(t) is a stochastic process. By taking a compound Poisson process as X(t), an interesting mathematical model is created.

Keywords

  • Sample Path
  • Wiener Process
  • Deterministic Function
  • Actual Expenditure
  • Independent Increment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1982 Springer-Verlag

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Park, C. (1982). Stochastic barriers for the Wiener process and a mathematical model. In: Chao, JA., Woyczyński, W.A. (eds) Martingale Theory in Harmonic Analysis and Banach Spaces. Lecture Notes in Mathematics, vol 939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096264

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  • DOI: https://doi.org/10.1007/BFb0096264

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11569-4

  • Online ISBN: 978-3-540-39284-2

  • eBook Packages: Springer Book Archive